Mixed Topic Worksheet Grades 8/9: Day 046
- 1
Question 1. y is directly proportional to x and inversely proportional to z.
y = 6 when x = 4 and z = 2.
Find the value of y when x = 10 and z = 4.Direct & Inverse Proportion with Functions▶ Show worked answerHide worked answer
- M1: 6 = k × 4 ÷ 2
- M1: y = 3 × 10 ÷ 4
- A1: 7.5
Answer: 7.5[3 marks] - 2
Question 2. A, B and C are points on a circle with AB = AC and angle BAC = 40°. TAU is the tangent at A, with T and C on opposite sides of AB. Work out the size of angle TAB. Give reasons.
Combining Circle Theorems▶ Show worked answerHide worked answer
- M1: triangle ABC is isosceles, so angle ACB = (180 - 40) ÷ 2
- B1: angle ACB = 70°
- A1: angle TAB = 70° (alternate segment theorem)
Answer: 70°[3 marks] - 3
Question 3. The equation x³ + 5x = 20 has a solution between x = 2 and x = 2.5
Use a change of sign to find this solution correct to 1 decimal placeChange of Signs▶ Show worked answerHide worked answer
- M1: f(x) = x³ + 5x - 20, test values between 2 and 2.5
- M1: f(2.1) = -0.239, f(2.15) = 0.688
- A1: sign change between 2.1 and 2.15 so 2.1
Answer: x = 2.1[3 marks] - 4
Question 4. ABCDEFGH is a cuboid. M is the midpoint of GH.
Work out the angle between AM and the plane ABCD.
Give your answer to 1 decimal place.3D Trigonometry▶ Show worked answerHide worked answer
- M1: AN² = (10 ÷ 2)² + 7²
- M1: AN = √74
- M1: tan MAN = dfrac6AN
- A1: angle MAN = 34.9
Answer: 34.9[4 marks] - 5
Question 5. Here is a speed-time graph for a train, with speed in metres per second and time in minutes. Use 4 trapezia of equal width to estimate the distance travelled in the 12 minutes, in metres.
Estimating Areas Under Curves▶ Show worked answerHide worked answer
- M1: 3 × (0 ÷ 2 + 9 + 12 + 9 + 0 ÷ 2) = 90
- M1: 90 × 60
- A1: 5400 m
Answer: 5400 m[3 marks]
Mixed Topic Worksheet Grades 8/9: Day 046
- 1
Question 1. y is directly proportional to x and inversely proportional to z.
[3 marks]
y = 6 when x = 4 and z = 2.
Find the value of y when x = 10 and z = 4.Direct & Inverse Proportion with Functions▶ Show worked answerHide worked answer
- M1: 6 = k × 4 ÷ 2
- M1: y = 3 × 10 ÷ 4
- A1: 7.5
Answer: 7.5 - 2
Question 2. A, B and C are points on a circle with AB = AC and angle BAC = 40°. TAU is the tangent at A, with T and C on opposite sides of AB. Work out the size of angle TAB. Give reasons.
[3 marks]Combining Circle Theorems▶ Show worked answerHide worked answer
- M1: triangle ABC is isosceles, so angle ACB = (180 - 40) ÷ 2
- B1: angle ACB = 70°
- A1: angle TAB = 70° (alternate segment theorem)
Answer: 70° - 3
Question 3. The equation x³ + 5x = 20 has a solution between x = 2 and x = 2.5
[3 marks]
Use a change of sign to find this solution correct to 1 decimal placeChange of Signs▶ Show worked answerHide worked answer
- M1: f(x) = x³ + 5x - 20, test values between 2 and 2.5
- M1: f(2.1) = -0.239, f(2.15) = 0.688
- A1: sign change between 2.1 and 2.15 so 2.1
Answer: x = 2.1 - 4
Question 4. ABCDEFGH is a cuboid. M is the midpoint of GH.
[4 marks]
Work out the angle between AM and the plane ABCD.
Give your answer to 1 decimal place.3D Trigonometry▶ Show worked answerHide worked answer
- M1: AN² = (10 ÷ 2)² + 7²
- M1: AN = √74
- M1: tan MAN = dfrac6AN
- A1: angle MAN = 34.9
Answer: 34.9 - 5
Question 5. Here is a speed-time graph for a train, with speed in metres per second and time in minutes. Use 4 trapezia of equal width to estimate the distance travelled in the 12 minutes, in metres.
[3 marks]Estimating Areas Under Curves▶ Show worked answerHide worked answer
- M1: 3 × (0 ÷ 2 + 9 + 12 + 9 + 0 ÷ 2) = 90
- M1: 90 × 60
- A1: 5400 m
Answer: 5400 m
Mixed Topic Worksheet Grades 8/9: Day 046
- 1
Question 1. y is directly proportional to x and inversely proportional to z.
y = 6 when x = 4 and z = 2.
Find the value of y when x = 10 and z = 4.Direct & Inverse Proportion with Functions▶ Show worked answerHide worked answer
- M1: 6 = k × 4 ÷ 2
- M1: y = 3 × 10 ÷ 4
- A1: 7.5
Answer: 7.5[3 marks] - 2
Question 2. A, B and C are points on a circle with AB = AC and angle BAC = 40°. TAU is the tangent at A, with T and C on opposite sides of AB. Work out the size of angle TAB. Give reasons.
Combining Circle Theorems▶ Show worked answerHide worked answer
- M1: triangle ABC is isosceles, so angle ACB = (180 - 40) ÷ 2
- B1: angle ACB = 70°
- A1: angle TAB = 70° (alternate segment theorem)
Answer: 70°[3 marks] - 3
Question 3. The equation x³ + 5x = 20 has a solution between x = 2 and x = 2.5
Use a change of sign to find this solution correct to 1 decimal placeChange of Signs▶ Show worked answerHide worked answer
- M1: f(x) = x³ + 5x - 20, test values between 2 and 2.5
- M1: f(2.1) = -0.239, f(2.15) = 0.688
- A1: sign change between 2.1 and 2.15 so 2.1
Answer: x = 2.1[3 marks] - 4
Question 4. ABCDEFGH is a cuboid. M is the midpoint of GH.
Work out the angle between AM and the plane ABCD.
Give your answer to 1 decimal place.3D Trigonometry▶ Show worked answerHide worked answer
- M1: AN² = (10 ÷ 2)² + 7²
- M1: AN = √74
- M1: tan MAN = dfrac6AN
- A1: angle MAN = 34.9
Answer: 34.9[4 marks] - 5
Question 5. Here is a speed-time graph for a train, with speed in metres per second and time in minutes. Use 4 trapezia of equal width to estimate the distance travelled in the 12 minutes, in metres.
Estimating Areas Under Curves▶ Show worked answerHide worked answer
- M1: 3 × (0 ÷ 2 + 9 + 12 + 9 + 0 ÷ 2) = 90
- M1: 90 × 60
- A1: 5400 m
Answer: 5400 m[3 marks]